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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 277200w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.w3 | 277200w1 | \([0, 0, 0, -9340050, -10986816125]\) | \(494428821070157824/77818125\) | \(14182353281250000\) | \([2]\) | \(5898240\) | \(2.5030\) | \(\Gamma_0(N)\)-optimal |
| 277200.w2 | 277200w2 | \([0, 0, 0, -9368175, -10917319250]\) | \(31181799673942864/387562277025\) | \(1130131599804900000000\) | \([2, 2]\) | \(11796480\) | \(2.8495\) | |
| 277200.w1 | 277200w3 | \([0, 0, 0, -17535675, 10979748250]\) | \(51126217658776516/25121936269815\) | \(293022264651122160000000\) | \([2]\) | \(23592960\) | \(3.1961\) | |
| 277200.w4 | 277200w4 | \([0, 0, 0, -1650675, -28366586750]\) | \(-42644293386916/29777663954115\) | \(-347326672360797360000000\) | \([2]\) | \(23592960\) | \(3.1961\) |
Rank
sage: E.rank()
The elliptic curves in class 277200w have rank \(0\).
Complex multiplication
The elliptic curves in class 277200w do not have complex multiplication.Modular form 277200.2.a.w
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
